Controlled competitive dynamics in a photorefractive ring oscillator: ‘‘Winner-takes-all’’ and the ‘‘voting-paradox’’ dynamics

Abstract

We investigate a system through which a variety of competitive dynamics can be optically realized. The interaction between the dynamical variables, in this case the intensities of resonator modes, can be controlled and even programmed. Photorefractive media are used to establish the coupling between the optical modes. We illustrate the properties of such a system through two different instances. The first is a ``winner-takes-all'' system in which the mutual competition between the modes leads to multiple stable fixed points in which one mode oscillates while the other ones are suppressed. The second system employs circular coupling between the modes giving rise to a dynamically recalled sequence of modes, often referred to as ``voting-paradox'' dynamics.